scholarly journals Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Matthew Rhudy ◽  
Yu Gu ◽  
Jason Gross ◽  
Marcello R. Napolitano
Keyword(s):  
Sensor Fusion ◽  
Unscented Kalman Filter ◽  
Attitude Estimation ◽  
Square Root ◽  
Fusion Algorithm ◽  
Matrix Square Root ◽  
Global Positioning ◽  
The Matrix ◽  
Aerial Vehicle ◽  
Diagonalization Method

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

Model aided airborne integrated navigation system based on an improved square-root unscented H∞ filter

2018 ◽  
Vol 41 (5) ◽  
pp. 1290-1300
Author(s):  
Jieliang Shen ◽  
Yan Su ◽  
Qing Liang ◽  
Xinhua Zhu
Keyword(s):  
Kalman Filter ◽  
Navigation System ◽  
Unscented Kalman Filter ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Strong Nonlinearity ◽  
Square Root ◽  
Integrated Navigation ◽  
Fusion Algorithm ◽  
Integrated Navigation System

An inertial navigation system (INS) aided with an aircraft dynamic model (ADM) is developed as a novel airborne integrated navigation system, coping with the absence of a global navigation satellite system. To overcome the shortcomings of the conventional linear integration of INS/ADM based on an extended Kalman filter, a nonlinear integration method is proposed. Fast-update ADM makes it possible to utilize a direct filtering method, which employs nonlinear INS mechanics as system equations and a nonlinear ADM as observation equations, substituting the indirect filtering based on linear error equations. The strong nonlinearity generally calls for an unscented Kalman filter to accomplish the fusion process. Dealing with the model uncertainty, the inaccurate statistical characteristics of the noise and the potential nonpositive definiteness of the covariance matrix, an improved square-root unscented H∞ filter (ISRUHF) is derived in the paper, in which the robust factor [Formula: see text] is further expanded into a diagonal matrix [Formula: see text], to improve the accuracy and robustness of the integrated navigation system. Corresponding simulations as well as real flight tests based on a small-scale fixed-wing aircraft are operated and ISRUHF shows superiority compared with the commonly used fusion algorithm.

SSP Podded Propulsion Motor Control Based on SR-CDKF

2014 ◽  
Vol 986-987 ◽  
pp. 1142-1145
Author(s):  
Wen Long Yao
Keyword(s):  
Qr Decomposition ◽  
Estimation Accuracy ◽  
Square Root ◽  
Rotor Speed ◽  
Closed Loops ◽  
Speed Controller ◽  
Sensorless Vector Control ◽  
Matrix Square Root ◽  
The Matrix ◽  
Vector Control System

In this paper,the rotor speed and the position of the SSP propulsion motor are estimated for building sensorless vector control system with speed and current double closed loops based on square root center difference Kalman filter (SR-CDKF) algorithm. This method makes use of the QR decomposition linear algebra techniques and so on, and it updates the matrix square-root of the state covariance by the Cholesky factor updating. This method can not only get the more steady results but also improve the estimation accuracy of the SSP podded propulsion system. Simulation result shows that the improved CDKF algorithm is not only more accurate but also has higher rate of convergence compared with CDKF speed controller.

A note on computing the matrix square root

CALCOLO ◽  
2003 ◽  
Vol 40 (4) ◽  
pp. 273-283 ◽  
Author(s):  
B. Iannazzo
Keyword(s):  
Square Root ◽  
Matrix Square Root ◽  
The Matrix

scholarly journals A Fault-Tolerant Multiple Sensor Fusion Approach Applied to UAV Attitude Estimation

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yu Gu ◽  
Jason N. Gross ◽  
Matthew B. Rhudy ◽  
Kyle Lassak
Keyword(s):  
Sensor Fusion ◽  
Fault Tolerant ◽  
Attitude Estimation ◽  
Single Frequency ◽  
Test Bed ◽  
Multiple Sources ◽  
Fusion Algorithm ◽  
Cost Rate ◽  
Fault Detection And Identification ◽  
Multiple Sensor

A novel sensor fusion design framework is presented with the objective of improving the overall multisensor measurement system performance and achieving graceful degradation following individual sensor failures. The Unscented Information Filter (UIF) is used to provide a useful tool for combining information from multiple sources. A two-step off-line and on-line calibration procedure refines sensor error models and improves the measurement performance. A Fault Detection and Identification (FDI) scheme crosschecks sensor measurements and simultaneously monitors sensor biases. Low-quality or faulty sensor readings are then rejected from the final sensor fusion process. The attitude estimation problem is used as a case study for the multiple sensor fusion algorithm design, with information provided by a set of low-cost rate gyroscopes, accelerometers, magnetometers, and a single-frequency GPS receiver’s position and velocity solution. Flight data collected with an Unmanned Aerial Vehicle (UAV) research test bed verifies the sensor fusion, adaptation, and fault-tolerance capabilities of the designed sensor fusion algorithm.

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